Abstract
The effect of disorder, both structural (non-diagonal) and on-site (diagonal), is studied through the inhomogeneous Bogoliubov-de Gennes (BdG) theory in narrow-band disordered superconductors with a view towards understanding superconductivity in boron doped diamond (BDD) and boron-doped nanocrystalline diamond (BNCD) films. We employ the attractive Hubbard model within the mean field approximation, including the short-range Coulomb interaction between holes in the narrow acceptor band. We study substitutional boron incorporation in a triangular lattice, with disorder in the form of random potential fluctuations at the boron sites. The role of structural disorder was studied through non-uniform variation of the tight-binding coupling parameter where, following experimental findings, we incorporate the concurrent increase in structural disorder with increasing boron concentration. We illustrate stark differences between the effects of structural and on-site disorder and show that structural disorder has a much greater effect on the density of states, mean pairing amplitude and superfluid density than on-site potential disorder. We show that structural disorder can increase the mean pairing amplitude while the spectral gap in the density of states decreases with states eventually appearing within the spectral gap for high levels of disorder. This study illustrates how the effects of structural disorder can explain some of the features found in superconducting BDD and BNCD films such as a tendency towards saturation of the Tc with boron doping and deviations from the expected BCS theory in the temperature dependence of the pairing amplitude and spectral gap.
Highlights
To illuminate the influence of structural disorder, we study the mean pairing amplitude, the distribution of pairing amplitudes, the spectral gap and the density of states while the boron concentration is fixed at 15 % and the structural disorder parameter is varied
While on-site potential disorder at the boron sites alone decreases the mean pairing amplitude and spectral gap, structural disorder can increase the mean pairing amplitude the spectral gap still decreases as the disorder parameter increases
This significant difference in behaviour stems from the introduction of states within the gap region in the case of structural disorder, resulting in a wide distribution of mean pairing amplitudes
Summary
The interplay of superconductivity and disorder close to the Anderson-Mott transition has long been of significant fundamental interest in understanding quantum phase transitions and emergent phenomena.[1,2,3] The pivotal role of disorder in these phase changes has come to the forefront as the influence of different forms of disorder are widely studied.[4,5,6,7,8,9] Studies of 2D localized superconductors using the Hubbard model with Anderson on-site disorder have shown that the spectral gap remains finite even at very high levels of disorder.[10,11,12] The transition from macroscopic superconducting coherence to localized regions with a finite pairing amplitude interspersed by insulating regions has been studied using the BdG theory as well as Monte Carlo analysis.[12].
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